According to Fun at Home With Kids, to make slime without borax, combine 2 and 1/4 cups of cornstarch, 1/2 cup of shampoo and 6 tablespoons of water. Add any liquid watercolors or food coloring to achieve the desired hue.
Use any type of shampoo for this recipe. Mix the food coloring or liquid watercolor with the shampoo prior to combining it with the cornstarch. After the color is thoroughly mixed into the shampoo, mix it into the cornstarch. The result will turn into small, crumbly pieces at first and should be able to be rolled into a ball. If it does not form into a ball, add a bit more cornstarch. If it does not shine or melt, add a bit more water.
If the slime is played with for an extended period of time or if it sits for awhile, more water may have to be added. Store this slime in a tightly sealed container. If the slime sits through the night, add 1/4 cup of water to make it slimy again. This slime should be able to be molded and pressed and then come back to its original shape. For instance, a child's hand print should slowly disappear.